The Morse potential U(r) that represents the energy of interaction between two atoms as a function of their separation r is often given by the equation:
U(r)=U0₀{exp[−2ar−r]−2exp[−a(r−r₀)]}
where U₀​, a, and r₀​ are constants. Given the relationship between energy and force dU/dr, and the differential form of Hooke's Law relating force F and stiffness E, determine the initial stiffness Einitial​ exhibited in a stress-strain test when r=r₀​.